Current Research - Antieigenvalues
Since 1948 the Kantrovich and Kantrovich-type inequalities for positive bounded operators have had many applications in operator theory and other areas of the mathematical sciences, such as statistics and numerical optimization. Antieigenvalue-type quantities and Kantrovich-type inequalities have numerous applications in statistics, operator theory, and numerical analysis. The "Two Nonzero Component Lemma (TNCL)," discovered and proved by myself, is a dimension reducing optimization tool and, as such, has applications in other areas of pure and applied mathematics. Currently I am investigating how TNCL can be used to compute closed form answers to some famous resource allocation problems.